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Anatoly S. Kondratiev

Anatoly S. Kondratiev
http://www.imm.uran.ru
Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences, Ekaterinburg, Russian Federation

Department of Algebra and Topology, Leading Researcher

PhD (Phys., Math.), Professor

ScopusID: 7005980596

ResearcherID: I-9622-2017

ORCID ID: 0000-0003-3073-3064

Scientific interests: Finite and Algebraic Groups, their Representations, Group Geometries

Scientific achievements: A series of the characterizations of finite non-solvable groups by the properties of Sylow or local subgroups is obtained; the decomposition matrices for a series of concrete quasisimple groups are calculated; finite linear groups of degree < 28 over fields and residue rings are described; a strengthened version of the well-known Sims conjecture on finite primitive permutation groups is proved; the description of connected components of prime graph for finite simple groups is completed; Mazurov's conjecture on the recognizability by spectrum all finite simple groups (besides A6) whose prime graph has at least three connected components is proved; well-known Gorenstein problem on the description of 2-signalizers in all finite simple groups is solved; normalizers of the Sylow 2-subgroups in finite simple groups are determined; a series of the characterizations of finite groups by the properties of their prime graphs is obtained; minimal finite non-supersolvable groups factorized by two their normal supersolvable subgroups are determined; the pronormality of subgroups of odd index in  finite simple groups is investigated.

Main publications:

 

  1. A.S. Kondrat'ev, A.A. Makhnev, A.I. Starostin. Finite groups.  J. Sov. Math. 1989. Vol. 44, no. 3, 237–318.
  2. A.S. Kondrat'ev. Subgroups of finite Chevalley groups.  Russian Math. Surv. 1986. Vol. 41, no. 1, 65–118.
  3. A.S. Kondrat'ev. Decomosition numbers of the group J2. Algebra and Logic. 1988. Vol. 27, no. 5, 333–349. 
  4. A.S. Kondrat'ev. On prime graph components of finite simple groups. Math. USSR Sbornik. 1990. Vol. 67, no. 1, 235–247.
  5. A.S. Kondrat'ev, V.I. Trofimov. Stabilizers of graph's vertices and a strengthened version of the Sims conjecture. Dokl. Math. 1999. Vol. 59, no. 1, 113–115.
  6. A.S. Kondrat'ev. Finite linear groups of small degree. II. Commun.Algebra. 2001. V.29, no. 9, 4103–4123.
  7. A.S. Kondrat'ev, A.E. Zalesskii. Linear groups of degree at most 27 over residue rings modulo pk. J. Algebra. 2001. Vol. 240, no. 1, 120–142.
  8. A.S. Kondrat'ev, V.D. Mazurov. 2-Signalizers of finite simple groups. Algebra i Logika. 2003. Vol. 42. no. 5, 594–623.
  9. A.S. Kondrat'ev. Normalizers of the Sylow 2-subgroups in finite simple groups. Math. Notes. 2005. V. 78, no. 3, 338–346.
  10. A.S. Kondrat'ev. Groups and Lie algebras. Ekaterinburg: UrO RAN, 2009, 310 p.